We review and synthesize recent developments in the study of the spread of invasive species, emphasizing both empirical and theoretical approaches. Recent theoretical work has shown that invasive species spread is a much more complex process than the classical models suggested, as long range dispersal events can have a large influence on the rate of range expansion through time. Empirical work goes even further, emphasizing the role of spatial heterogeneity, temporal variability, other species, and evolution. As in some of the classic work on spread, the study of range expansion of invasive species provides unique opportunities to use differences between theory and data to determine the important underlying processes that control spread rates.

Understanding the dynamics of small populations is obviously important for declining or rare species but is also particularly important for invading species. The Allee effect, where fitness is reduced when conspecific density is low, can dramatically affect the dynamics of biological invasions. Here, we summarize the literature of Allee effects in biological invasions, revealing an extensive theory of the consequences of the Allee effect in invading species and some empirical support for the theory. Allee effects cause longer lag times, slower spread and decreased establishment likelihood of invasive species. Expected spatial ranges, distributions and patterns of species may be altered when an Allee effect is present. We examine how the theory can and has been used to detect Allee effects in invasive species and we discuss how the presence of an Allee effect and its successful or unsuccessful detection may affect management of invasives. The Allee effect has been shown to change optimal control decisions, costs of control and the estimation of the risk posed by potentially invasive species. Numerous ways in which the Allee effect can influence the efficacy of biological control are discussed.

Migratory animals are comprised of a complex series of interconnected breeding and nonbreeding populations. Because individuals in any given population can arrive from a variety of sites the previous season, predicting how different populations will respond to environmental change can be challenging. In this study, we develop a population model composed of a network of breeding and wintering sites to show how habitat loss affects patterns of connectivity and species abundance. When the costs of migration are evenly distributed, habitat loss at a single site can increase the degree of connectivity (mixing) within the entire network, which then acts to buffer global populations from declines. However, the degree to which populations are buffered depends on where habitat loss occurs within the network: a site that has the potential to receive individuals from multiple populations in the opposite season will lead to smaller declines than a site that is more isolated. In other cases when there are equal costs of migration to two or more sites in the opposite season, habitat loss can result in some populations becoming segregated (disconnected) from the rest of the network. The geographic structure of the network can have a significant influence on relative population sizes of sites in the same season and can also affect the overall degree of mixing in the network, even when sites are of equal intrinsic quality. When a migratory network is widely spaced and migration costs are high, an equivalent habitat loss will lead to a larger decline in global population size than will occur in a network where the overall costs of migration are low. Our model provides an important foundation to test predictions related to habitat loss in real-world migratory networks and demonstrates that migratory networks will likely produce different dynamics from traditional metapopulations. Our results provide strong evidence that estimating population connectivity is a prerequisite for successfully predicting changes in migratory populations.

Summary 1.There are very few general guidelines available to improve the process of eradicating invasive species. We addressed the basic question of whether it is more efficient to prioritize the removal of outliers or core populations of an invasive grass, Spartina alterniflora . 2. We used a structured model in which the population of the invasive species is partitioned into different classes based on local conspecific density in order to investigate density-based eradication strategies. 3. The Spartina population at a Pacific coast estuary in Washington state, USA, is subject to an Allee effect: at low density plants produce fewer propagules than in high-density coalesced meadows. Plants at low density, however, are able to spread faster vegetatively. We used a genetic algorithm to find the optimal division of resources between removal of high-density and low-density plants. We explored the consequences of the Allee effect, contrasting financial budgets available for control operations and the inclusion of seedling control in addition to the control of mature plants. 4. We found that the optimal strategy was dependent on the annual budget available for control. At low and medium budgets, it was necessary to remove the low-density plants first to achieve eradication, but if more money was available then the optimal strategy was to prioritize high-density areas. 5. Without an Allee effect the optimal strategy would always be to prioritize the removal of fast-growing, low-density sub-populations. Seedling control did not change the optimal strategy but did, in some cases, reduce the cost of eradication. 6. Synthesis and applications . Given the uncertainty in future budgets allocated for control of invasive Spartina , we recommend a strategy that prioritizes the removal of lowdensity subpopulations of S. alterniflora over high-density subpopulations. The Allee effect in this system is not sufficiently strong to outweigh the importance of the rapid vegetative spread of the plants at low density.

It is usually assumed that pollen availability does not limit reproduction in wind-pollinated plants. Little evidence either supporting or contradicting this assumption exists, despite the importance of seed production to population persistence and growth. We investigated the role of pollen limitation in an invasive estuarine grass (Spartina alterniflora), with a manipulative pollen supplementation and exclusion experiment in areas of high population density and at the low-density leading edge of the invasion. We also quantified pollen deposition rates on stigmas and pollen traps along a windward to leeward gradient. We found pollen impoverishment at the low-density leading edge of a large invasion, causing an 8-fold reduction in seed set. We found 9-fold more pollen on stigmas of high-density plants than on those of lowdensity plants. Pollen deposition rates on stigmas and traps did not increase downwind of low-density plants but did increase downwind of high-density plants and dropped off precipitously across a gap that lacked pollen donors. The delay of appreciable numbers of seed caused by pollen limitation persists for decades until vegetative growth coalesces plants into continuous meadows, and this Allee effect has slowed the rate of spread of the invasion.